Hi Iceland,
Willy is in Zhongshan, so he could tell you more than I could. I live in Hong Kong, so I can tell you a bit. I take the ferry from the China Ferry Terminal in Kowloon (one every 2 hours, 1 hr 45 min journey), but I’m pretty sure there is a ferry straight from the airport, which avoids you having to go through customs more than once. I doubt if you need to book. The Zhongshan ferry is a fair distance from Zhongshan, so you will probably need a taxi. Don’t know the hotel. Ask Willy.
Don’t know how you are getting to Guangzhou from Zhongshan, but if it is by train, you will probably end up at Guangzhou main station or Guangzhou East. Just take the metro to Guangzhou South. You should be able to get a ticket no problem. 2 hours 20 minutes to Changsha South. Get an official taxi to the hotel (about 30 rmb). Don’t go to the taxi touts. There are many good cheap hotels in Changsha from about 130 yuan upwards.
Don’t know about the other cities you mentioned, but can say a bit about train travel. I like travelling on overnight trains. For example the Shenzhen to Changsha train takes 10 hours. Seats costs 115rmb (not advised), Hard Sleepers cost 200/206/213 rmb (6 narrow berths, 2 triple-deckers, no door to cabin, open to corridor, ok, but no privacy and quite cramped), Soft sleepers cost 308/322 rmb (4 berths, 2 double-deckers, wider, quite comfy, cabin has door, very nice.) To Guilin, you should be able to get the equivalent, and it will be way cheaper than the flight. You can only get tickets up to 10 days in advance. They usually only take cash. To avoid big queues at the station ticket office, you can pay 5rmb or so more and got to a ticket shop.